V^cAl-IIO
AEE No. L5F01
1
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
If
WARTIME REPORT
ORIGINALLY ISSUED
June I9U5 as
Advance Has trie ted Beport L5FOI
COLUMN AND PLATE COMPEESSIVE STRENGTHS
OF AIRCRAFT STRUCTURAL MATERIAI£
2l^S-T ALUMINUM- ALLOY SHEET
By Eugene E. Lundquist, Evan H, Schuette,
George J. Heimerl, and J. Albert Ro/
Langley Memorial Aeronautical Laboratory
Langley Field, Ya.
UNtVERSlTY OF FLOPiDA
DOCUMENTS DEPARTMENT
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P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA
WASHINGTON
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\-x3 y^'? ^'^'^ •?sO*^7^ 1
NAG A A.^R No. L^FOl
NATIONAL ADVISORY COMMITTEE FOR /iERONAUTICS
ADVA^IGE RESTRICTED -JEPORT
COLUMI AND PLATE COMPRESSIVE STRENGTHS
OF AIRGR/iFT STRUG TUR..L MATERIALS
2I4.S-T ALUMINUM- ALLOY SHEET
By Eugene E. Lundquist, Evan H. Schuette
George J. Heimerl, and J. Albert Roy
SIJIViMARY
Column and plate compressive strengths of 2lj.S-T alu-
minum-alloy sheet were determined both within and beyond
the elastic r^nge from tests of thin-strip columns and
from local-instability tests of formtad 2- and channel-
section columns. These tests are the first of a series
in an extensive research investigation to provide data
on the structural strength of various aircraft m.aterials.
The results, which are pre>-ente5. in the form of curves
and charts that may be used in the design and analysis
of aircraft structures, supersede preliminary results
published previousl^f.
INTRODUCTION
Column and plate members in an aircraft structure are
the basic elements that fail by instability. If efficient
structures are to be designed, the strength of these ele-
ments must be known for the various aircraft materials.
Aji extensive research program has therefore been under-
taken at the Langley Memorial Aeronautical Laboratory to
..establish the column and plate compressive strengths for
a number of the alloys available for use in aircraft
structures. Reliable and rapid pi-'ocedures for testing
such matei'isls have already been developed and are
described in referencjes 1 and 2.
The first m.aterlal tested during the present investi-
gation was 2[t.3-T aluminum- alloy sheot. The results for
this material, given herein, supersede those contained
In a preliminary report (reference 2).
2 NAG A ARR No. L^FOl
SYMBOLS
L length of column
p rr^dius of gyrstion
c fixity coefficient used in Suler column formula
— p effective slenderne^s I'-atio of thin-stx-'io column
p^fc
b width of piste
brp width of flfinge of Z- or channel section (see fig. 1)
b™ width of web of Z- or channel section (see fig. 1)
r inside radius of bend of Z- or channel section
(see fig. 1)
t thickness of pl-^te
k nondimensional coeffj.cient used in plate-buckling
formula
k^ coefficient k used with bjy- pjid t in plate -
buckling formula (see fig. 2 and reference 3)
Sq modulus of elasticity in comoression, taken as
10,700 ksi for ^i+S-T aluminum alloy
T nondimensional coefficient for columns (The value of
T is so determined that when the effective
modulus TE(, is substituted for En in the
equation for elastic buckling of columns, the
computed critical stress agrees with the
experimentally observed value. The coefficient t
is equal to unity within the elastic range and
decreases with Increasing stress beyond the elastic
range. )
r\ nondimensional coefficient for plates corresponding
to T for colu:nns
|j, Pois son's ratio, taken as O.3 for 2[|.S-T alumlniun alloy
NAG A AR'R No. L5F01
^ Q-p criticsl coiTiprsssive stress
<7^„„ sver^ee comoressiva stress at inaximurn load
o compressive yisld stress
]\STHODS OP TESTING M3D ANALYSIS
All tests were irisde in hydraulic testing machines
accurate to within three-fourths of 1 percent. The ends
of the stress-strain specimens and the colunins were ground
flat end square.
Stress-stra in curves .- The compressive stress-strain
data, which identify the material for correlation v/ith
its column and plate compressive strengths, were obtained
from tests of single -thickness sceclinens in a compression
fixture of the Montgomery-Temp lin type shovm in figure 5'
This fixture v/as used only for flat compression specimens,
which represented the material before forming. Infor-
mation on the teclinique used in maklnn these tests is
presented in reference Ij.. For the bent material in the
corners of the formed Z- and channel sections, compression
specimens were cut from^ the corner portion and tested in
the special fixture shoivn in figure k.
Column strength. - The column strength and the asso-
ciated effective column modulus were obtained by testing
thin-strip columns of the m^aterial with the ends clamped
in fixtures of the type shown in figure 5. The use of
end fixtures of this type is discussed in detail in
reference 1. The fixtures used have been improved, and the
method of analysis has been modified since the publication
of reference 1. The method now used results in a columji
curve representative of nearly perfect column specimens.
In addition, the miethod now takes into account the fact
that columns of the dimensions tested are actually plates
with two free edges.
Plate compressi ve stre ngcii.- The plate compressive
strength of 'the material was obtained from compression
tests on Z- and channel-section columns so proportioned
as to develop local instability, that is, instability of
the plate elements of which they are comiprised. (See
fig. 6.) Inasmuch as the flanges and webs of such columns
are in reality plates with various ■ kinds of edge suoport.
i| KAGA ARR No. L5?01
the problem cf Iccel instability of these colur.ms Is a
plete-buckllng pi'obleiii, aiicl tiie plate compressive strength
of the ..ripterlal wss evsluated frcm these tests. The
lengtlis of the colurniis were so chosen as to avoid colunxi
faiiui'e and still provide satlsf actoi^y local- Inatfbllity
data. These conslderptious ere discussed in reference 5»
The Z- and chaiinel-section cclanms were tested v/ith
the ends bearing directly agginst the testing-machine
heads, which were carefully alined to insure uniform
bearing on the colamia ends. A Z-section colioirji urider
test is shov.n in figure 7« Th'- relative displacemencs of
pointers, which 'vvera supported by extension arms attached
to the fl-snges of the specimens, were measiared by the
cpticfl -Tiicroirietyrs thet can bo seen in figure 7* Ttie
displacement was taken as a measure of the cross-sectional
distoi'tion, and the critical compressive stress was obtained
from stress-distortion curves of the type illustrated in
figure 3, The critical stress y»as determined as the
stress at the point near the top of the iaiee of the stress-
distortion curve at vjhich a marked increase in distortion
first occurred w3 th sm.all increase in stress. (See fig. 3.)
RESULTS AJTD DISCXjSSIOK
Because the compressive properties of aluminxxm-alloy
sheet may vary appreciabl;/ , the data and charts of the
present report should not be applied to the desifxi of
structures of 2IlS-T aluminum- allov sheet having compressive
properties appreciably different from those reported
herein unless a suitable method is devised for adjusting
test x'-esalts to account for variations in material
properties.
Compressive Stress-Strain Curves
Com.pressive stress-strain curves obtained for tne
flat sheet material used in marine; the colui:Xi3 are given
in figure Q for both directions of grain. The Z-, channel,
or thin-strip colutmis to which a particular stress-strain
curve applies are indicated in table 1, to^^ether with the
value of the coiiipressive yield stress CJ^^. for that stresS'
strain curve. These values average approximately i|Ij. ksi
for the flat sheet material in the v/ith-grrdn direction
NAG A ARR No. L5F01 5
and Ij.9 Ksl in the cross -grain direction. The modulus of
elasticity in compression v/as taken as 10,700 ksi, the
accepted value for 2lj.S-T aluminum alloy.
When the flat sheet mrterial is bent to an inside
radius r of Jt to form a Z or channel, the cold vifork
done on the material evidently raises the compressive
yield stress for the curved corner portion above that for
the flat web or flange, about lei percent for the with-
grain and 10 percent for the cross-grain direction. (See
fig. 10. ) Because the curved corner specimens included
along their edges some flat material (about 1^.0 percent
of the total area) for which the yield stress is lower
than that for the curved portion, the actual increase in
the compressive yield stress for the corner portion may
be scir-ewhat greater than the Increase indicated in fig-
ure 10. The important result to note is that the com-
pressive properties of a formed section may not be uniform
over the cross section.
Col^ormi Stz-'ength
The results of the tests of the thin-strip columns
are given by the coluinn curves of figure 11 for the two
directions of grain.
At stresses beyond the elastic range, the experi-
mental values of a^^^ are lov/er than those computed by
the Euler column formula (see elastic-buckling curve,
fig. 11), because of the I'eduction in the effective
modulus of elasticity. The effective modulus to be
substituted for E^ in the Euler coluirm formula to bring
calculatsd and experimental values of o^^ into agreement
is givexi as tEc where t Is a coefficient that is equal
tc unity in the elastic range and decreases with Increasing
stress beyond the elastic range. In structural calculations
in vifhlch it is impossible to use directly values obtained
from the column curve (fig. 11), the value of t for a
given stress must be known. The variation of t with
stress for columns is therefore showi in figure 12 for
both directions of grain.
D
NACA ARR Uo. LSFOl
Fl?fcF> ComnressT ve 3tren.2;th
The i-esults o'f ths local-instability tests of the
forined Z- rnd chaixne 3 -section col''aiiii"s , used to determine
the plate compressive strength, ar'e Piver. in tables 2
and 5. The important ralationcbips for corr.pressed platos
obtained from these testr are sho«vn on the curves ajid
design charts presented in the follov.'in^ paragraohs.
Plate-buck] ing c urve . - The plate-buckling curve,
which is analo.:ous to the colur::n .curve , is shovm in fig-
ure 15 for olstes loaded in the wlth-grain direction.
The abscissa Ir figure I3 is suggested by transposing the
plate-buckling equation
cr
krr^^t-
12(l-i..^)b'
(1)
to the form
a.
cr
TT^Hl,
----|2
(2)
whore the subscript W is added to r.aice the terms b
and k of the equation correspond to the entries in
tables 2 smd 5« The siir.ilarity between the form of
equation (2) .and the follovv'lng form of the 3uler colur.xi
for.iuls 1? to be noted:
cr
■J
C
Vp,v
(5)
At stresses bejor.d the elastic range, as in the case
cf colii/iins, the experimental values of Q for plates
are lovvex* than those given by equation (2) for clastic
buck]. ing (see elastic-bucicling curve, fig. 15), because
of the reduction in the effective modulus of elasticity.
The effective plate modulus corresoonding to tS_ for
columns is rlv-n as rS
c»
rnd the varlftion ol
c
r
th
NACA ARR No. L5FOI (
stress is given, togethex" with the variation of t, in
figure 12. The crossing of tne t_ and r:-curves shown
in figure 12 occurs because the formed columns apparently
had an appreciable degree of imperfection, which resulted
in the deviation of the r,- curve from unity at a lower
stress than that at which th3 T-curve, reoresentative
of nearly perfect columns, deviates from unity.
Relationshio of a to o_„/n for plates.- In
cr cr
problems concerned with the strength of plates, it is
sometimes desirable to insert the value of nS^ for E^
in the plate-buckling formula, equation (1), and to write
the eqiistion in the transposed form
('-^)
In this form the v?lue of "^cr/^^ ^-'^ given by the modulus
of elasticity, Poisson's ratio, the ji.eometric dimensions
of the elate, and the coefficient Ic, The value of a^^
can then be obtplned by use of the curve of o^^ against
o^-p/v given in figure l!|. This curve m.ay be obtained by
plottinT the data directly or by plotting from the faired
curves of figure 15.
As in the case of equation (1), the subscripts W
may be added to k end b of equation (I).), and ^cr^''^'
m.ay be determined for a Z- or channel-section by the use
of the formula and curve of figure 2.
Maximum compressive strength of plate elements . - In
the case of a plate loaded in long i tud in a 1 c ompre s s i on ,
the supported, or restrained and supported, side edges
remain essentially straight after buckling and ore capable
of carrying additional load. As a consequence, there is
a 'maximum strength for the plate that is greater than
the buckling strength.
Theoreticrl studies that appear in the literature
concerning the ultimate strength of plates and the asso-
ciated effective width of the plates after buckling
indicate that the average stress at miaxiraum load is
related to the critical stress. It is therefore reason-
able to assum.e that the average stress at maximmn loed
8 FACA .Al^R No. L5FOI
a„, „^ for tli-^ co'.nbinatiori of "olgte elsL-'ents that ms-ke up
the 2- or chc'<rinel-sec tloii oolu.ia 11 slso related to tho
criticril str^ess for the ccmbinstlori . Accoriingly, tns
e.xeri:-.ner,t£l veluos obtcvinad era plotted in figure I5
as o^.^ sgap'nst the r.9t:*o ^cr/^r:irx5 ^nd from thi:; ^^S~
ure a definite ralptior:ship ii s 3e:. to exist between
o^r, and '^r.iax ^-^ ^ given ve-lu3 of by;/t.
In corra c?S3F. , vcl.ies of "j.v.p;. r ether thsn ^cr
may be requi^-'ed in strength c£-lcalption:; . fj-.e values of
a.--^gy are therefore plotted against ^crA) ^^' ^'ifc^ii'"- 16.
The fe3sibility of making such a plot is indicated by the
rel.atlorshio bet'Ji/een o^v, aiid '^oxv'V shovVi'i in fii^ure 1I4.
and the I'elaticnship betv:een a.jia" ^^'^'^ "^cr sbo'Vn in
fiprure 15 . Figure 16 is i?articulsrlv useful because tne
qumitiby '^cr/''^ ^*-^ doterrninod by Imomi quantities
a-^cordlng to the fori!;ula fnd cur/-3 of figure 2.
The ressc-n for the diff^vrence in the curves of fig-
ures 15 and 16 for difTorent values of b.. /t is not
fiilly uTiderstocd. Tro s tress-str ■oa.n curves hi-ve indicated,
nowever^ that the bevidlng of the naterial in the for:r.ing
of the colunns raises the compressive yield stress for the
ma^'erial in tiie corners. ( 3ee fig. 10.) An exeunination
of the data Gliowed thct rs b'..-/t :s reduced for a given
thickness t and a given value of c^cr/hj the total cross-
sectional ax'^ea is also redj.ced; the fixed area of high-
strength tent matei'isl in the corners therefoi-e becoT.es a
higher rercentage of the total eres. This fact .may account
for the hi;Ther values of a^ax obtained at given values
of '^crAl '^''•*' "t-^'"^ Z- and cnannsl-section columns 'vith
lo'.ver values of b-j/t. (See fig, 16.)
Zf fee t of gr a i n d i ^0 c 1 1 on on plate s t r en .c t h . - The
data on plate strength '^rssen ted in figures IJ to lo were
obtained from columns loaded in the wibh-grain direction.
In order to deter^:ine_the effect of grain direction on the
values of o^r' f^'id ^v.ax» a ^'sw coliAjmas were constructed
pj.id tested with the grain of the sheet at right angles
to the axis of the col'jurji. These columns are herein
designated cross -gr fin columns.
In figurot. I7 and 1,,., th^ aata obtained from the
cross-grain columns are plotted as exoer-mental joints
NACA AP.Vx Ho. L5F01 9
for comparison with curves taken from figures iL. snd l6
for the with-grain colioinns. Only at the higher stresses,
where the stress-strain curva i'or the cross-grain direction
differs noticeably from tne stress-strain curve for_the
with-srain direction, are the values of o and a „„,,
' cr max
greater for the cross-grain columns than for the with-grain
columns. The average increase in the high-stress region
was about I4. percent for o and about 2 percent for '^rpax'
vifhereas the cross-grain compressive yield stress was approx-
imately 11 percent greater than the with-grain compressive
yield stress.
Ch. arts f o r loc a 1 in s t^ab i lity of Z- aj:;d channel-section
columns.- Th.e olaFe~compre"ssive strength of the materi al
was evplu^ted from tests of Z- and channel-section columns.
The results of these tests, which provided this information
regarding olates, may also be applied directly to formed
Z- and channel-section col'Jini:i3 that fail by local insta-
bility. These results can be conveniently sujuraarized in
the form of charts that give directly, in terins of the
dimension ratios bp/b;sr and b-,:/t, the critical stress
and the average stress at maximum load. Such charts,
based on the theoretical curve of figure 2 and the experi-
m^ental data, are given in figures I9 to 21.
COWGLUDING REMARK
The important conclusions of this report are em.bodied
in the test data of column and plate compressive strengths,
which are presented in the form of curves and charts that
may be used in the design 9nd analysis of aircraft
structures of 2l|S-T aluminum- alloy sheet.
Lsngley ]V-eraori?l Aaron ^^utical Lr.borat»ry
N-'tional Advisory Comi.iittcje iov Aoronautics
Langley Field, Va.
13 NACA art; Y.o. I.5?01
Lundoui=:.t, R\x::er,B E., RossjT'Sn, Csrl A., nncl Houlolt,
JoVin G-: A Riethod. fo-' DsDei'ml/iinp- the Colurrm
Ci;rv3 frcin Tests of Columns vrith Equal Restraints
ai?iast Rotation cr. the Ends. iMCA Til No. ^OJ,
heliiiPrlj George J., and Roy, ■!. AlbO'rt: ih'-elitnlnsry
Report on Tests of 2l|.S-T Alurr.lniiiii- Alloy Coluii;ns of
Z-, Cnrnnel, ^nd E-Seotion That Develop Locrl
In£t?biJlty, IIA^^'A ?.3V.o. JJZ'?, lSl|5 •
•vrollj A. C. , risiiOi^, Gordon P., and Heiirnerl, George ^
Charts for Cr'lcalrtion of the Critical Stress for
Locrl Instability cf GolUinns v,ith I-, Z-, Ghsnnel,
sna Rect£:n,!?:ui&r-Tub9 oectl-.)n. ,NACA ARR ?\^o. JKOIl,
■9i
1
LL
iSiiJ.
Kotonchi':, Joseph lu , Woods, waiter, rnd Weinberger,
Robert A. : InvOBtigatlcn of r.-3thods of Supporting
S.lnj^le-lhiclcness Specimens m e. Fixture for DeterrrJ.'
nation of Corirpre3s;ive Stress-Str^^an Curves. KAGA
No. T,5E1S , 19': 5.
t31
Keimerl, George J., tnd Roy, J. Albert: Determinstion
of Desii'pble Lengths of Z- and Chf'imel-Section
Colunins for Locai-Instfjbility Tests. NAG A H3
No. lIilUO, IPL4.
MCA .-iRR No. L5F01 11
TABLE 1.- CO!l'PRESSI"'''E PROPERTIES OF 2i|S-T ALUIvIBITOJ-ALLOY SHEET
[e^ = 10,700 ksi]
Co:
.umns to whic
h stress- strt.in
1 Compressive yield
curve E
apoly
Stress-
strain
ST^^aGSS^ f*lA
■
Type
Direotion
of
loading
Designation
( See tables 2 and 3)
curve
(fig. 9)
iVith
grain
(ksi)
Cross
grain
(ksi)
Thin
"'ith grain
All
A
U2.9
U7.9
strip
and cross
grain
Z
'.'Vith grain
la to 6a, 6c, 7a, 10a,
10b, 11a to 19a, 26b,
27a, 27c, 28a, 29a,
31b to 32c
B
UU.o
U6.e
Z
Vvith grain
6b, 7t to 9, 10c, 19b
C
i+6.3
51.3
to 26a, 26c, 27b, 2et,|
280, 29b to 31a
Z
Cross
grain
la to Uc
D
U3.i+
Ue.5
Channel
I'.ith grain
1 to 6a, 7a, 8a, 9a,
10a, 11a, 12a, 13a,
llj-a, 15a, l6a, 17a,
18a, 19a, 20a, 21a,
21b, 22a, 23a, 21+^,
25a, 27a to 28a, 2Qa,
30a to 31a, 32a, 33a,
5l4.a, 35a, 36a
E
U3.i4
i|6.9
Channel
'Vith grain
6b, 6c, 7b, 7c, 8b,
8c, 9b, 9c, 10b, 10c,
lib, lie, 12b, 12c,
13 b, 13 c, lUb, li4c,
15b, 15c, I6b, I6c,
17b, 17c, 18b, lec,
19b, 19c, 20b, 22b,
23 b, 23 c, 2l;b, 2i;c,
25b, 25c, 26a, 26b,
28b, 29b, 29c, 31b,
32b
F
Uh.3
UQ.7
Channel
Vi'ith grain
31c, 32c, 33b, 3^'C,
3Ub, 35b, 36b. 36c
G
U3.9
ii7.9
Channel
Cross
grain
la to L|.c
D
k3'U
1
US. 5
NACA aRR No. L5F01
12
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COMMinEE FOR AERONAUTICS
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NACA ARR No. L5F01
Fig. 2
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Fig. 3a, b
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NACA ARR No. L5F0]
Fig. 5
NATIONAL ADVISORY
COMMinEE rOR AERONAUTICS
Figure 6 ~ Typical cross -sectional distortion
of columns that develop local instability.
NACA ARR No. L5F01
Fig. 7
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NACA ARR No. L5F01
Fig. 8
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Fig. 9
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NACA ARR No. L5F01
Fig. 11
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NACA ARR No. L5F01
Fig. 13
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Fig. 19
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NATIONAL ADVISORY
COMMinEE FOR AESONAUTICS
Rgure 19. - Design chart for a^p ^o^ formed Z45-T
alurninum - alloij Z- and channel -sec+ion colunnns that
develop local instabilittj loaded in the with -grain
direction
CTq^
= 44 ksi.
NACA ARR No. L5F01
Fig. 20
60
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Figure 20.- Design chart for CT>„ax for formed 24S-T
aluminum - alloy Z- section columns that develop local
instability loaded in the with- groin direction *, 0'j.ys44ksi
NACA ARR No. L5F01
Fig. 21
60
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Figure Zl. - Design chart for o-j^qx for formed Z45-T
aluminum - alloy channel - section columns that develop
locol instability loaded in the with -grain direction j
<Tcy = 44 ksi
I
UNIVERSITY OF FLORIDA
3 1262 08106 493 2
UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
RO. 30X117011
GAINESVILLE. FL 32611-7011 USA
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